Question

The quadratic polynomial f(x) = ax + bx+c has real zeroes a and B. If a, b,c are real and of
same sign then
(A) a > 0.B < 0
(B) B > 0. a>0
(C)a <0.> 0
(D) B<0. a<0​

Answer 1

Two main keys

'a, b, c has same sign' & 'D>0'

If we let f(x)=0 and use the relationship

we will be given

α+β=$-\frac{b}{a}$ --- 1

αβ=$\frac{c}{a}$ --- 2

Since a, b, c have same sign,

α+β<0 (∵1)

αβ>0 (∵2)

We are given multiplication and sum

Since α, β are real

∴α, β are both negative.

∴α<0, β<0

So option D is correct answer